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Comment by uryga | Hacker News Reader

Okay, my wording wasn't the best here. 3d doesn't "have" 2 planes. But, for some reason, you can look in any direction in 3d by turning in two planes. Test it yourself: turning your head left-right is rotation in one plane, turning it up-down is rotation in the other plane. here's my shot at illustrating this: https://goo.gl/photos/Cxt7KPbos5o2QnkD9

to be completely honest, I'm not sure if this intuition is correct. But it seems to make sense

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I don't think that's correct. You can also rotate around the direction you are looking.

Rotations in 2D are one-dimensional. Complex numbers are two-dimensional but we fix one degree of freedom by fixing the length.

Rotations in 3D are there-dimensional. Quaternions are four-dimensional but we fix the length again.

It's correct that you can look in any direction with only two planes, but that's not enough; you need to be able to control your orientation around that final axis. You need 3 planes for that (3 "rotational degrees of freedom"). The idea that a quaternion is somehow two complex numbers is wrong.

Thanks. I did some research and found out that, indeed, my vague understanding of quaternions was wrong. I remember skimming the Wikipedia article and seeing this: https://en.m.wikipedia.org/wiki/Quaternion#Quaternions_as_pa...

I then assumed that my idea with two rotations is how quaternions work. Here's to actually reading about a concept before I start explaining it next time...

I think you can do that using two rotation axis only (cf. proper Euler angles).

And quaternions are made of two complex numbers.

edit: typo.

>And quaternions are made of two complex numbers.

I don't pretend to grok quaternions (I only use them), but I'm fairly sure a quaternion consists of three imaginary numbers plus a real number.

Sure, but the way they play together can also be expressed by the means of two complex numbers (which makes 4 real numbers in total).

This is not true. You can't factor a quaternion into two complex numbers. Please don't spread misinformation.

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